Applying the geometric mean theorem and the Pythagorean theorem, we have: x = 16; y = 20; z = 15.
What is the geometric mean theorem?
The geometric mean theorem states that: altitude / left = right / altitude.
In this case, we are given the following:
left = x
right = 9
Altitude = 12
Plug in the values:
12/x = 9/12
Cross multiply:
144 = 9x
144/9 = x
x = 16
Use Pythagorean theorem to find y and z respectively:
y = √(12² + 16²)
y = 20
z = √(12² + 9²)
z = 15